The present invention relates to a method for transmitting symbols of non-binary error-correcting code words via a communication channel. These codes are defined over non-binary sets. The invention has applications for example in the transmission of non-binary LDPC (Low Density Parity Check) codes or Reed-Solomon codes. The invention also relates to the corresponding transmitted signal and the receiving of such a signal.
The invention will be more particularly described in the context of non-binary LDPC codes. LDPC codes are known error-correcting codes for approaching the theoretical Shannon limit. Because of their performance in terms of noise immunity, LDPC codes and particularly non-binary LDPC codes have applications in many systems, for example wireless communication systems, optical fiber, cable, digital data storage systems, etc.
Non-binary LDPC codes, also known as NB-LDPC codes, are constructed in a non-binary Galois field of order q, conventionally denoted GF(q). The order q is generally a power of 2, for example q=2p. An LDPC code in GF(q) is defined by a sparse parity check matrix H of size A×B whose elements belong to GF(q), where A is the number of parity constraints and B is the number of elements of GF(q) in the code word. For a Galois field GF(4) composed of 4 elements {0, α0, α1, α2}, the parity matrix for A=3 and B=6 is for example as follows:
  H  =      (                            0                                      α            0                                                α            0                                    0                                      α            2                                    0                                                  α            1                                    0                          0                                      α            0                                    0                                      α            2                                                            α            0                                    0                                      α            2                                    0                          0                                      α            1                                )  
This matrix can also be represented by a bipartite graph (Tanner graph) with A parity nodes and B variable nodes receiving the symbols of the code word. Each column of the parity matrix is associated with a variable node and each row of the matrix is associated with a parity node.
In order to transmit them on a communication channel that is usually noisy, it is known to modulate non-binary LDPC codes with an M-ary orthogonal spread-spectrum modulation as described in the document entitled “Combine Non-Binary LDPC codes with M-ary orthogonal spread spectrum modulation”, Yu-zhen Huang, Yun-peng Cheng, Yu-ming Zhang, Guo-hai Yu, Jin Chen, 2010 International Conference on Wireless Communications and Signal Processing (WCSP), 2010. The use of a spread spectrum modulation provides better noise immunity.
In particular, this document discloses modulating the symbols of NB-LDPC code words with an orthogonal spread spectrum modulation using 2M Walsh-Hadamard sequences that are orthogonal to each other, with 2M equal to the order q(=2p) of the Galois field GF(q) of the non-binary LDPC codes, and M equal to the number p of bits of each symbol of the Galois field GF(q). The size 2M of the constellation of the orthogonal modulation is taken as equal to the number q=2p of symbols of the field of NB-LDPC codes so that there is no loss of information in the demodulation. In that document, the demodulation is relatively complex to implement, as it requires cross-correlation calculations between each of the 2p Walsh-Hadamard sequences and the noisy signal, which has a cost in terms of implementation. In that document, the demodulation is performed by means of 2p matched filters each associated with a predetermined Walsh-Hadamard sequence. One aim of the invention is to overcome the above disadvantage.